13) Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
Question
- Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
Solution
Step 1: Identify the total number of outcomes. In this case, there are 20 tickets, so there are 20 possible outcomes.
Step 2: Identify the favorable outcomes. These are outcomes where the ticket drawn is a multiple of 3 or 5. The multiples of 3 between 1 and 20 are 3, 6, 9, 12, 15, and 18. The multiples of 5 between 1 and 20 are 5, 10, 15, and 20.
Step 3: Remove the duplicates from the favorable outcomes. In this case, 15 is a multiple of both 3 and 5, so we only count it once. So the favorable outcomes are 3, 6, 9, 12, 15, 18, 5, 10, and 20.
Step 4: Count the number of favorable outcomes. In this case, there are 9 favorable outcomes.
Step 5: Calculate the probability. The probability of an event is the number of favorable outcomes divided by the total number of outcomes. So the probability of drawing a ticket that is a multiple of 3 or 5 is 9/20 = 0.45.
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